Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11719433 | C2 | semidirect |
| 3. C13×#497 | C2 | semidirect |
| 4. #11718848 | C2 | semidirect |
| 5. #11718843 | C2 | semidirect |
| 6. #11718834 | C2 | semidirect |
| 7. #11718824 | C2 | semidirect |
| 8. #11718747 | C2 | semidirect |
| 9. #11718716 | C2 | semidirect |
| 10. #11718375 | C2 | semidirect |
| 11. #11718366 | C2 | semidirect |
| 119. #497 | D13 | semidirect |
| 225. C13 | #3216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719433 | 2 |
| #11719373 | 2 |
| C13×#497 | 2 |
| #11718848 | 2 |
| #11718843 | 2 |
| #11718834 | 2 |
| #11718824 | 2 |
| #11718747 | 2 |
| #11718716 | 2 |
| #11718375 | 2 |
| #11718366 | 2 |
| #3216 | 13 |